Finite Group Databasebeta

← C3×C5×#1615 #14274649

Subgroups — C3×C5×#1615 #14274649

Order 1920.

416 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#539C211yesmaximal, characteristic
2C3×C5×#484C211yesmaximal, characteristic, complemented
3C3×C5×#481C211yesmaximal, characteristic
4C3×C5×#400C211yesmaximal, characteristic, complemented
5C3×C5×#328C211yesmaximal, characteristic, complemented
6C3×C5×#327C211yesmaximal, characteristic
7C3×C5×#324C211yesmaximal, characteristic, complemented
8C5×#1615C311yesmaximal, characteristic, direct product factor, Hall
9C3×C5×#126—21no—
10C3×C5×#125—21no—
11C3×C5×#123—21no—
12C3×C5×#123—21no—
13C3×C5×C22⋊Q8—21no—
14C3×C5×C22⋊Q8C2211yescharacteristic
15C3×C5×#121C2211yescharacteristic
16C3×C4×C5×D4—21no—
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C3×C5×#107—21no—
20C3×C5×#106—21no—
21C3×C5×#103—21no—
22C3×C5×#102—21no—
23C3×C5×C22⋊C8C2211yescharacteristic
24C3×C5×C22⋊C8C2211yescharacteristic
25C3×C5×#95—21no—
26C3×C5×#95—21no—
27C3×C5×#95C2211yescharacteristic
28C3×#1615C511yesmaximal, characteristic, direct product factor, Hall
29C5×#539C2×C311yescharacteristic
30C5×#484C2×C311yescharacteristic, complemented
31C5×#481C2×C311yescharacteristic
32C5×#400C2×C311yescharacteristic, complemented
33C5×#328C2×C311yescharacteristic, complemented
34C5×#327C2×C311yescharacteristic
35C5×#324C2×C311yescharacteristic, complemented
36C2×C3×C5×Q8D411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4D411yescharacteristic
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5D411yescharacteristic
43C22×C3×C4×C5D411yescharacteristic
44C22×C3×C4×C5C2311yescharacteristic
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C4⋊C4D411yescharacteristic
56C3×C5×C4⋊C4D411yescharacteristic
57C3×C5×C22⋊C4—21no—
58C3×C5×C22⋊C4—21no—
59C3×C5×C22⋊C4—21no—
60C3×C5×C22⋊C4—21no—
61C3×C5×C22⋊C4—21no—
62C3×C42×C5—21no—
63C3×#539C2×C511yescharacteristic
64C3×#484C2×C511yescharacteristic, complemented
65C3×#481C2×C511yescharacteristic
66C3×#400C2×C511yescharacteristic, complemented
67C3×#328C2×C511yescharacteristic, complemented
68C3×#327C2×C511yescharacteristic
69C3×#324C2×C511yescharacteristic, complemented
70C5×#126—21no—
71C5×#125—21no—
72C5×#123—21no—
73C5×#123—21no—
74C5×C22⋊Q8—21no—
75C5×C22⋊Q8C22×C311yescharacteristic
76C5×#121C22×C311yescharacteristic
77C4×C5×D4—21no—
78C2×C5×C4⋊C4C22×C311yescharacteristic
79C2×C5×C4⋊C4C22×C311yescharacteristic
80C5×#107—21no—
81C5×#106—21no—
82C5×#103—21no—
83C5×#102—21no—
84C5×C22⋊C8C22×C311yescharacteristic
85C5×C22⋊C8C22×C311yescharacteristic
86C5×#95—21no—
87C5×#95—21no—
88C5×#95C22×C311yescharacteristic
89#1615C3×C511yescharacteristic, direct product factor, Sylow
90C23×C3×C5—21no—
91C23×C3×C5C2×D411yescharacteristic
92C3×C5×Q8—41no—
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C3×C5×D4—41no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—42no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5—81no—
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C3×C5×C8—41no—
114C3×C5×C8—41no—
115C3×#126—21no—
116C3×#125—21no—
117C3×#123—21no—
118C3×#123—21no—
119C3×C22⋊Q8—21no—
120C3×C22⋊Q8C22×C511yescharacteristic
121C3×#121C22×C511yescharacteristic
122C3×C4×D4—21no—
123C2×C3×C4⋊C4C22×C511yescharacteristic
124C2×C3×C4⋊C4C22×C511yescharacteristic
125C3×#107—21no—
126C3×#106—21no—
127C3×#103—21no—
128C3×#102—21no—
129C3×C22⋊C8C22×C511yescharacteristic
130C3×C22⋊C8C22×C511yescharacteristic
131C3×#95—21no—
132C3×#95—21no—
133C3×#95C22×C511yescharacteristic
134C2×C5×Q8C3×D411yescharacteristic
135C2×C5×D4—21no—
136C2×C5×D4C3×D411yescharacteristic
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5C3×D411yescharacteristic
141C22×C4×C5C3×D411yescharacteristic
142C22×C4×C5C23×C311yescharacteristic
143C2×C5×C8—21no—
144C2×C5×C8—21no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4—21no—
147C5×C4⋊C4—21no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4—21no—
150C5×C4⋊C4—21no—
151C5×C4⋊C4—21no—
152C5×C4⋊C4—21no—
153C5×C4⋊C4C3×D411yescharacteristic
154C5×C4⋊C4C3×D411yescharacteristic
155C5×C22⋊C4—21no—
156C5×C22⋊C4—21no—
157C5×C22⋊C4—21no—
158C5×C22⋊C4—21no—
159C5×C22⋊C4—21no—
160C42×C5—21no—
161#539C2×C3×C511yescharacteristic
162#484C2×C3×C511yescharacteristic, complemented
163#481C2×C3×C511yescharacteristic
164#400C2×C3×C511yescharacteristic, complemented
165#328C2×C3×C511yescharacteristic, complemented
166#327C2×C3×C511yescharacteristic
167#324C2×C3×C511yescharacteristic, complemented
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5—41no—
171C22×C3×C5—41no—
172C22×C3×C5—41no—
173C22×C3×C5#12011yescharacteristic
174C22×C3×C5#13511yescharacteristic
175C22×C3×C5#13711yescharacteristic
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—41no—
179C3×C4×C5—41no—
180C3×C4×C5—41no—
181C3×C4×C5—41no—
182C3×C4×C5—41no—
183C3×C4×C5—81no—
184C3×C4×C5—81no—
185C2×C3×Q8C5×D411yescharacteristic
186C2×C3×D4—21no—
187C2×C3×D4C5×D411yescharacteristic
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4C5×D411yescharacteristic
192C22×C3×C4C5×D411yescharacteristic
193C22×C3×C4C23×C511yescharacteristic
194C2×C3×C8—21no—
195C2×C3×C8—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4C5×D411yescharacteristic
205C3×C4⋊C4C5×D411yescharacteristic
206C3×C22⋊C4—21no—
207C3×C22⋊C4—21no—
208C3×C22⋊C4—21no—
209C3×C22⋊C4—21no—
210C3×C22⋊C4—21no—
211C3×C42—21no—
212C23×C5—21no—
213C23×C5C2×C3×D411yescharacteristic
214C5×Q8—41no—
215C5×D4—41no—
216C5×D4—41no—
217C5×D4—41no—
218C2×C4×C5—21no—
219C2×C4×C5—21no—
220C2×C4×C5—21no—
221C2×C4×C5—21no—
222C2×C4×C5—21no—
223C2×C4×C5—21no—
224C2×C4×C5—21no—
225C2×C4×C5—41no—
226C2×C4×C5—41no—
227C2×C4×C5—41no—
228C2×C4×C5—41no—
229C2×C4×C5—42no—
230C2×C4×C5—41no—
231C2×C4×C5—41no—
232C2×C4×C5—81no—
233C2×C4×C5C2×C3×D411yescharacteristic
234C2×C4×C5C2×C3×D411yescharacteristic
235C5×C8—41no—
236C5×C8—41no—
237#126—21no—
238#125—21no—
239#123—21no—
240#123—21no—
241C22⋊Q8—21no—
242C22⋊Q8C22×C3×C511yescharacteristic
243#121C22×C3×C511yescharacteristic
244C4×D4—21no—
245C2×C4⋊C4C22×C3×C511yescharacteristic
246C2×C4⋊C4C22×C3×C511yescharacteristic
247#107—21no—
248#106—21no—
249#103—21no—
250#102—21no—
251C22⋊C8C22×C3×C511yescharacteristic
252C22⋊C8C22×C3×C511yescharacteristic
253#95—21no—
254#95—21no—
255#95C22×C3×C511yescharacteristic
256C2×C3×C5—21no—
257C2×C3×C5—21no—
258C2×C3×C5—81no—
259C2×C3×C5#45211yescharacteristic
260C2×C3×C5#45411yescharacteristic
261C2×C3×C5#45811yescharacteristic
262C23×C3—21no—
263C23×C3C2×C5×D411yescharacteristic
264C3×Q8—41no—
265C3×D4—41no—
266C3×D4—41no—
267C3×D4—41no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—42no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—81no—
283C2×C3×C4C2×C5×D411yescharacteristic
284C2×C3×C4C2×C5×D411yescharacteristic
285C3×C8—41no—
286C3×C8—41no—
287C22×C5—21no—
288C22×C5—21no—
289C22×C5—41no—
290C22×C5—41no—
291C22×C5—41no—
292C22×C5C3×#12011yescharacteristic
293C22×C5C3×#13511yescharacteristic
294C22×C5C3×#13711yescharacteristic
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—41no—
298C4×C5—41no—
299C4×C5—41no—
300C4×C5—41no—
301C4×C5—41no—
302C4×C5—81no—
303C4×C5—81no—
304C2×Q8C3×C5×D411yescharacteristic
305C2×D4—21no—
306C2×D4C3×C5×D411yescharacteristic
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4C3×C5×D411yescharacteristic
311C22×C4C3×C5×D411yescharacteristic
312C22×C4C23×C3×C511yescharacteristic
313C2×C8—21no—
314C2×C8—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4C3×C5×D411yescharacteristic
324C4⋊C4C3×C5×D411yescharacteristic
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C42—21no—
331C3×C5#161511yescharacteristic, direct product factor, Hall
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—41no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3C5×#12011yescharacteristic
338C22×C3C5×#13511yescharacteristic
339C22×C3C5×#13711yescharacteristic
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—41no—
345C3×C4—41no—
346C3×C4—41no—
347C3×C4—81no—
348C3×C4—81no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5—81no—
352C2×C5C3×#45211yescharacteristic
353C2×C5C3×#45411yescharacteristic
354C2×C5C3×#45811yescharacteristic
355C23—21no—
356C23C2×C3×C5×D411yescharacteristic
357Q8—41no—
358D4—41no—
359D4—41no—
360D4—41no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—81no—
376C2×C4C2×C3×C5×D411yescharacteristic
377C2×C4C2×C3×C5×D411yescharacteristic
378C8—41no—
379C8—41no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—81no—
383C2×C3C5×#45211yescharacteristic
384C2×C3C5×#45411yescharacteristic
385C2×C3C5×#45811yescharacteristic
386C5C3×#161511yescharacteristic, direct product factor, Sylow
387C22—21no—
388C22—21no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22C3×C5×#12011yescharacteristic
393C22C3×C5×#13511yescharacteristic
394C22C3×C5×#13711yescharacteristic
395C4—21no—
396C4—21no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—81no—
403C4—81no—
404C3C5×#161511yescharacteristic, direct product factor, Sylow
405C2—21no—
406C2—21no—
407C2—81no—
408C2C3×C5×#45211yescharacteristic
409C2C3×C5×#45411yescharacteristic
410C2C3×C5×#45811yescharacteristic
subgroupG/H
center, socleC22×C3×C5#120
commutator, Frattini, cosocleC22×C4C23×C3×C5
prime radicalC3×C5×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3×C5 ◁ C22×C3×C4×C5 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C3×C5×#484C2semidirect
4. C3×C5×#400C2semidirect
5. C3×C5×#328C2semidirect
7. C3×C5×#324C2semidirect
8. C5×#1615C3direct (N × H)
28. C3×#1615C5direct (N × H)
30. C5×#484C2×C3semidirect
32. C5×#400C2×C3semidirect
33. C5×#328C2×C3semidirect
35. C5×#324C2×C3semidirect
64. C3×#484C2×C5semidirect
66. C3×#400C2×C5semidirect
67. C3×#328C2×C5semidirect
69. C3×#324C2×C5semidirect
89. #1615C3×C5direct (N × H)
162. #484C2×C3×C5semidirect
164. #400C2×C3×C5semidirect
165. #328C2×C3×C5semidirect
167. #324C2×C3×C5semidirect
331. C3×C5#1615direct (N × H)
386. C5C3×#1615direct (N × H)
404. C3C5×#1615direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×C5×#5392
C3×C5×#4842
C3×C5×#4812
C3×C5×#4002
C3×C5×#3282
C3×C5×#3272
C3×C5×#3242
C5×#16153
C3×#16155